Re: higher-order logic

From: alex goldman (hello_at_spamm.er)
Date: 01/30/05 

Date: Sun, 30 Jan 2005 10:22:21 -0800

Jose Juan Mendoza Rodriguez wrote:

>
> alex goldman wrote:
>
>> I'm interested in learning more about higher-order logic
>> (...)
>> Does anyone have any suggestions or links to resources?
>
> This is a very readable introduction to higher-order
> intuionistic logic:
>
> Simon Thompson, 'Type Theory and Functional Programming'
> http://www.cs.kent.ac.uk/people/staff/sjt/TTFP/
>

Thanks. I've read some of it, however, while I asked for pointers to
literature on higher-order logic, this paper discusses first-order logic.
And, while it's not a research paper plug, it does seem to be Constructive
Mathematics advocacy and mainly concerns itself with programming aides,
does it not?

I was hoping to find a non-advocacy review of main results in higher-order
logic (as opposed to first-order logic).

By the way, is the term "higher-order logic" ever used in a sense different
from "second-order logic"? Since second-order logic allows quantification
over relations, would third-, etc. order logics allow quantification over
quantifiers or something similarly outlandish?

Relevant Pages

  • Re: higher-order logic
    ... 'Type Theory and Functional Programming' ... And, while it's not a research paper plug, it does seem to be Constructive ... Since second-order logic allows quantification ... over relations, would third-, etc. order logics allow quantification over ...
    (sci.logic)
  • Re: Rules of deduction.
    ... derived from words in spoken language, eg. if, not, all, some. ... The rules of inference in symbolic logic are derived from methods ... it is very interesting to see how quantification differs ... modern logics. ...
    (talk.origins)
  • Re: In the empty domain:
    ... Paul Holbach wrote: ... >> of quantification may ... > due to there being nothing in the empty domain by definition. ... Owen might like to look at logics which do. ...
    (sci.logic)